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6. Let the utility function be U (31, m2) = 31n m1+ 31m $2 + 2. (a) Suppose that the budget line is I = mm + ngg. Find the optimal bundle of consumption as a function of I, 331, and 332. Show details. (1 point) (c) If s = 0, then (c1, Cg) = (II/phfg/pg) is the corresponding consumption bundle on the budget line. (b) Suppose that the budget line is 2 = $1 + $2 for $1 (-2 [0,1] and 2 = (1+ n + mg for $1 > 1. Here, 7' > 0 is a quantity tax imposed on all units of good 1 if $1 > 1. i. Find the optimal bundle of consumption. Show details. (2 points) ii. Sketch carefully the budget line, the indifference curve, and the optimal so- lution. Clearly label your graph. (1 point) (c) Suppose that the budget line is 2 = m1+m2 for m1 (-2 [0, 0.5] and 2 = (1 +T)m1+m2 for $1 > 0.5. Here, '7' > 0 is a quantity tax imposed on all units of good 1 if 31 > 0.5. i. Find the optimal bundle of consumption. Show details. (2 points) ii. Sketch carefully the budget line, the indifference curve, and the optimal so- lution. Clearly label your graph. (1 point)